Black technology starts from the steel suit

Chapter 244

Mass gap and nuclear energy

The establishment of the standard model is another very grand story, so I won’t talk about it here. Here I will talk about an issue that has to be discussed: the issue of quality.

Above we know that fermions are the particles that make up matter, and bosons are the particles that transmit the interaction force.For example, two electrons transmit electromagnetic force by exchanging photons, and two quarks transmit strong force by exchanging gluons, then photons and gluons are gauge bosons that transmit electromagnetic force and strong force respectively.

However, have you ever considered the quality of bosons?What happens if the mass of the boson that transmits the interaction force is too large or too small?

Still take the skating rink pass as an example, assuming that two people are standing on the skating rink to pass basketball to each other, then at first they will retreat because of the momentum of the basketball (this is the performance of repulsion), thus opening the distance, but they will always Back off slowly like this?
of course not!When the distance between the two is far enough, you can't shoot the basketball to me at all, then I won't back down.Think again, what if instead of a basketball you shot a shot put?Then maybe when we are still very close, your shot put will not be able to hit me.

In the model of the skating rink, the ball is the boson that transmits the force. If you cannot catch the ball, it means that the force cannot be transmitted to you, which means that its force range is limited.From the comparison between the basketball and the shot put, we can also clearly know that the greater the mass of the boson, the shorter the force range, and the smaller the mass, the longer the force range. If the mass of the boson is zero, then the force range is Infinity.

So, why is the electromagnetic force a long-range force that can travel far?Because the photon that transmits the electromagnetic force has no mass.But we also know clearly that the strong force and the weak force are only confined in the nucleus, that is to say, the strong force and the weak force are both short-range forces. Therefore, according to our above analysis, it seems that the bosons that transmit the strong force and the weak force should It has quality, and only with quality can it correspond to short-range force.

However, when Yang Zhenning was studying the gauge field, he found that to make the system have local gauge invariance, the mass of the gauge boson that transmits the force must be zero.That is to say, if the gauge boson has mass, it will break the local gauge symmetry.

Why does local gauge symmetry require bosons to have zero mass?You can think of it this way, what is local gauge symmetry?That is, different places are doing different transformations. Since the transformations in different places are different, there must be an intermediate messenger to convey this state, so that everyone can coordinate their work, otherwise you will jump yours and I will jump. Isn't mine messed up?
Well, since this courier is going to transmit state in different places (maybe two very far places), according to the above analysis, should it have zero mass?Only when the quality is zero can you run far~
Therefore, after this analysis, we will find that the correspondence between the local gauge symmetry and the zero mass of the gauge boson is very natural.However, this has caused the current dilemma: the local gauge symmetry requires that the gauge boson has zero mass, but the fact of the short-range force of the strong force and the weak force seems to require that the corresponding gauge boson must have mass, what should we do? ?
This problem not only troubled Yang Zhenning, it also troubled Pauli (in fact, there were only a few of them who were interested in gauge fields at that time).

Pauli was also very interested in gauge fields (Chen-ning Yang became interested in gauge fields only after reading Pauli’s 1941 paper), but when Pauli discovered this seemingly unsolvable quality problem, He gradually lost interest in the gauge field, and was unable to derive the final equation.

Yang Zhenning’s situation is slightly different. His mathematical foundation is very good, and his in-depth understanding of group theory can give him a deeper understanding of symmetry problems (think about the time when physicists didn’t like group theory, and Pauli took the lead. Call group theory the curse of groups).

In addition, in terms of aesthetics, Yang Zhenning is a die-hard fan of Einstein, and they are all staunch supporters of "symmetry determines interaction", which makes Yang Zhenning have a mysterious love for gauge fields.Moreover, Yang Zhenning was only about 30 years old at that time, which was the peak period of energy and creativity of scientists, so he was naturally fearless.

Therefore, Yang Zhenning has been frantically looking for the Yang-Mills equation. After finding the equation, even though he knew that there were unresolved quality problems, he still decided to publish his paper.

In his eyes, this equation and this set of theories are the perfect representation of "symmetry determines interaction" in his heart. Like Einstein, he firmly believes that God likes simplicity and beauty, and that God's simplicity and beauty are determined by precise symmetry.If so, then what better picture of the mind of God than the Yang-Mills theory based on this deep symmetry of gauge invariance?
Yang Zhenning's deep understanding of symmetry makes him have very strong confidence in the Yang-Mills theory. As for the quality problems shown in the strong and weak forces, it is just some problems in the application level of this theory.

The strong and weak forces are much more complicated than the electromagnetic force, so using Yang-Mills theory to explain the strong and weak forces will naturally not be as simple as dealing with the electromagnetic force.Why is the electromagnetic force so simple?If you think about it, electrons have electric effects, and the movement of electrons produces magnetic effects. The interaction between electrons is transmitted through photons, the gauge bosons, so the essence of electromagnetic force is the interaction between electrons and photons.

Here there is only one particle electron, and one gauge boson photon, and the photon still has no mass. If you look at the strong force, there are three kinds of colored quarks and eight different kinds of gluons. This is definitely much more complicated than the electromagnetic force!
Therefore, what Yang Zhenning thinks is: Yang-Mills theory is fine, but now it has some problems when it is applied to strong and weak forces (the quality problem is the biggest one in the early days), which is also natural.These are problems, not mistakes. With the deepening of people's research in the future, these problems should be gradually solved.

The development of history is indeed like this. The quality problems were solved by some other means later, so how were the quality problems finally solved?

In the quantum chromodynamics describing the strong force, we notice that the gluons that transmit the force between quarks are originally zero-mass, and zero-mass is compatible with gauge symmetry.But, if this is the case, the zero-mass boson should correspond to the long-range force, why is the strong force a short-range force (only valid in the nucleus)?

This involves a unique property of force: asymptotic freedom.Asymptotic freedom says that when the distance between quarks is very far, the force between them is very strong, as if no one can separate them, but once they are really brought together and the distance is very close, they The interaction force between them becomes very weak, as if the quark on the opposite side has nothing to do with it, a pair of quark lovers who are alive and well.In this way, in quantum chromodynamics, there is no conflict between the zero-mass gauge boson and the strong short-range force.

Asymptotic freedom explains why gluons have zero mass but the strong force is a short-range force, then the W and Z bosons that transmit the weak force have mass.If there is mass, the short-range force is easy to explain, but we said above that gauge bosons with mass will destroy the gauge symmetry. This gauge symmetry is the foundation of Yang-Mills theory. If it is destroyed, how can it be played?
The last solution to this problem is the Higgs mechanism.The Higgs mechanism is here to smooth things over: your Yang-Mills theory requires gauge bosons to have zero mass, but in the end we measured that W and Z bosons have mass, so what should we do?

Simple, I think that the gauge bosons W and Z, which transmit the weak force, have zero mass when they are born, but after they come to this world, they slowly gain mass for some reason, which means that their mass is not born It is given by the day after tomorrow, so that it neither conflicts with Yang-Mills theory nor with actual measurement.

So, the Higgs mechanism is actually the mechanism that endows particles with mass.It thinks that our universe is full of Higgs field, if the particle does not interact with the Higgs field, its mass is zero (such as photon, gluon), if the particle interacts with the Higgs field, then It has mass, and the stronger the effect, the greater the mass obtained.

It should be noted that not all the mass comes from the interaction between particles and the Higgs field, and part of it comes from the interaction between particles.

In July 2012, scientists finally found the Higgs particle at the Large Hadron Collider (LHC), which brought this story to a successful end and naturally reserved the 7 Nobel Prize in Physics. .

In this way, the Yang-Mills theory can completely describe the strong force, weak force and electromagnetic force, and completed the renormalization of the non-Abelian gauge field in Hoft (renormalization simply means that the theory can calculate meaningful Numerical values, rather than meaningless results like infinity, which is a common problem with point particle models.

To give the simplest example, we all know that the closer the charges are, the greater the electromagnetic force between them, so when the distance between charges approaches zero, will the electromagnetic force become infinite?This is a thinking question~) After that, the standard model of particle physics will be officially put into production and commercial use.

So far, our story about Yang-Mills theory has come to an end. I believe that those who can insist on reading here should have a general understanding of Yang-Mills theory, and they will have their own opinions on its function and significance. judge.

Mr. Yang Chenning is our national treasure-level scientist, and the Yang-Mills theory is the brightest pearl in his work so far. (In view of the basic and forward-looking nature of Mr. Yang’s work, many of his theories were not taken seriously when they were first proposed. , only to find it extremely important decades later, so I’m not sure anything more important than Yang-Mills theory will ever come along).

Noether discovered the relationship between symmetry and conservation laws, opening the door to symmetry in modern physics.

Einstein was keenly and deeply aware of this, and then applied it to the theory of relativity with a thunderous force. The great success he achieved stunned other scientists at that time.

But this routine is familiar to Einstein, and other people are not familiar with it. Besides, in the era of quantum revolution, Einstein is the "negative teaching material" for those quantum revolutionaries, and Bohr is their pope, so people don't bother to talk to you. Play.

Yang Zhenning can be said to be a direct disciple of Einstein. If Einstein is partial to symmetry, then Yang Zhenning has a soft spot for symmetry.He fully absorbed Einstein's symmetry idea, carried it forward, absorbed Weyl's gauge symmetry idea, and finally created the comprehensive Yang-Mills theory.

After the Yang-Mills theory came out, symmetry was no longer a toy for one person. Through this theory, Yang Zhenning turned a high-level elite product such as symmetry into a civilian toy that anyone can play with. The way to release the energy contained in the symmetry has been standardized, instrumentalized, and streamlined.

Since then, "symmetry determines interaction" is no longer a slogan, but has become the consensus and the most basic guiding ideology of physicists, which greatly released the productivity of physicists and laid the foundation for the rapid construction of the Standard Model. base.

This part is the most easily overlooked part when everyone is talking about the work of Mr. Yang Zhenning and Yang-Mills theory. If you can’t realize the importance of symmetry in modern physics, you can’t recognize Mr. Yang Zhenning and Yang-Mills The role of theory on the problem of symmetry, then your understanding of Mr. Yang's work is very one-sided, and even missed his most essential part.

The Higgs mechanism, asymptotic freedom, quark confinement, spontaneous symmetry breaking, and renormalization of the gauge field, these wonderful stories from Yang-Mills theory to the standard model seem to be more suitable for storytelling. Remember that symmetry is at the heart of modern physics.

Mr. Yang Zhenning is a very great physicist. In addition to his great academic achievements, his academic attitude is also very worthy of further study.

After a deep understanding, you can clearly feel that Mr. Yang has the advantages of Chinese education and Western education at the same time. He very effectively avoids the dross in Eastern and Western education, so Mr. Yang can always look ahead. to some key issues.

Of course, there are still some problems, such as the solution of the Yang-Mills equation.

There are still some unexplained problems, which may need to be completely typed out to be able to solve one of the seven major problems.

Or it is necessary to solve this problem before we can build a bridge between strong force and electromagnetic force!
Simply, he seems not far away from the answer now.

Picking up the pen and paper in his hand, Wang Feng thought about it and started to check the calculation.

This equation, which most people would feel a headache after seeing it, is so precious to Wang Feng!
(End of this chapter)